Role of interband and photoinduced absorption in the nonlinear refraction and absorption of resonantly excited PbS quantum dots around 1550 nm

The nonlinear refractive index ${n}_{2}$ and absorption coefficient $\ensuremath{\beta}$ of PbS quantum dots (Qdots) is determined around 1550 nm with the $Z$-scan technique, using a picosecond pulsed laser. We find that ${n}_{2}$ is wavelength tunable and follows the PbS absorbance spectrum. At fixed wavelength, ${n}_{2}$ is constant in the optical intensity range used (1--25 MW/cm${}^{2}$), indicative of a third order nonlinear effect. The figure of merit is larger than 1 in the quoted intensity range, demonstrating that PbS Qdots are efficient nonlinear materials at telecom wavelengths. It is argued that the creation of excitons and the resulting photoinduced absorption in the PbS Qdots lie at the origin of the observed ${n}_{2}$ and $\ensuremath{\beta}$. Analyzing the measured intensity dependence of the absorption at the first energy transition using a rate-equation model with a full bleaching at 4 excitons per Qdot, we find that photoinduced absorption inhibits the full bleaching of the Qdot first energy transition. Femtosecond four-wave mixing (FWM) experiments at low intensities show that the dynamics of the nonlinear optical response shows a nanosecond decay, which is attributed to exciton thermalization, while at higher excitation intensities an additional $\ensuremath{\sim}$100 ps component appears, which reflects carrier-carrier assisted processes. The analysis of the phase of the FWM signal shows that at high excitation the signal is dominated by photoinduced absorption once charge separation occurs. Considering the facile (wet) processing of colloidal Qdots, these results demonstrate the potential of PbS Qdots for low-cost photonic devices.